Matrix problems and stable homotopy types of polyhedra

This is a survey of the results on stable homotopy types of polyhedra of small dimensions, mainly obtained by H.-J. Baues and the author [3, 5, 6]. The proofs are based on the technique of matrix problems (bimodule categories). Dedicated to C. M. Ringel.     

Liquid Co–Sn alloys at high temperatures: structure and physical properties

The Co–Sn system is an important subsystem for Sn-based anode materials of lithium-ion batteries. Experimental results on the physical–chemical properties of this system in the liquid state, however, are rather sparse. In this work, the atomic structure and structure-sensitive thermophysical properties (viscosity, electrical resistivity, and thermoelectric power) of liquid Co–Sn alloys were investigated in a wide temperature range with special attention to the melting-solidification region. The obtained experimental results were combined with differential thermal analysis (DTA) data in order to verify the liquidus curve in the Sn-rich part of the Co–Sn phase diagram.     

Molecular dynamics investigation of the transient regime in the freezing of salt clusters

Molecular dynamics (MD) investigations of the freezing of supercooled liquids can identify nuclei far smaller than can be detected in laboratory experiments, to date, and consequently can provide information about nucleation so far inaccessible to experiment. In a recent MD study of the freezing of clusters of SeF6, a new method of recording nucleation events was introduced. It involved the observation of times of first appearance of nuclei of the size of n. An advantage of the new approach is that it provides information about the size of the critical nucleus. For nuclei smaller than the critical size, it also avoids the overshoots of nucleation rates that precluded the application of the Miloshev-Wu method in the subcritical region. Kinetic information in the transient regime can be characterized by three parameters, the time lag, the reduced moment, and the steady state nucleation rate. To get some idea of how general the new approach is, a very different system was investigated, that of clusters of NaCl. Two different fitting functions were used to analyze the results. The first one adopted the log-normal probability distribution of Wu. The second function was a modification of Shneidman's analytical solution appropriate for large nuclei. The second function gave a rather good account of MD data for all nuclear sizes and temperatures and gave more stable results in the subcritical region. Several inferences of the sizes of critical nuclei were made. Applying the criterion for n* based on the Zeldovich solution of the Becker-D?ring equations, we estimated the critical nucleus sizes to be 14, 18, and 24 ions for quench temperatures of 640, 690, and 740 K, respectively. Even though the interionic interactions initiating nucleation in salt are very different from the van der Waals interactions in clusters of SeF6, the characteristic aspects of the transient regimes of the two systems were quite similar.     

Rare earth-nickel-indides Dy5Ni2In4 and RE4Ni11In20 (RE=Gd, Tb, Dy)

The new rare earth metal (RE)-nickel-indides Dy₅Ni₂In₄ and RE₄Ni₁₁In₂₀ (RE=Gd, Tb, Dy) were synthesized from the elements by arc-melting. Well-shaped single crystals were obtained by special annealing sequences. The four indides were investigated by X-ray diffraction on powders and single crystals: Lu₅Ni₂In₄ type, Pbam, Z=2, a=1784.2(8), b=787.7(3), c=359.9(1) pm, wR₂=0.0458, 891 F² values, 36 variables for Dy₅Ni₂In₄, U₄Ni₁₁Ga₂₀ type, C2/m, a=2254.0(9), b=433.8(3), c=1658.5(8) pm, β=124.59(2)°, wR₂=0.0794, 2154 F² values, 108 variables for Gd₄Ni₁₁In₂₀, a=2249.9(8), b=432.2(1), c=1657.9(5) pm, β=124.59(2)°, wR₂=0.0417, 2147 F² values, 108 variables for Tb₄Ni₁₁In₂₀, and a=2252.2(5), b=430.6(1), c=1659.7(5) pm, β=124.58(2)°, wR₂=0.0550, 2003 F² values, 109 variables for Dy₄Ni_10.80In_20.20. The 2d site in the dysprosium compound shows mixed Ni/In occupancy. Most nickel atoms in both series of compounds exhibit trigonal prismatic coordination by indium and rare earth atoms. Additionally, in the RE₄Ni₁₁In₂₀ compounds one observes one-dimensional nickel clusters (259 pm Ni₁-Ni₆ in Dy₄Ni_10.80In_20.20) that are embedded in an indium matrix. While only one short In₁-In₂ contact at 324 pm is observed in Dy₅Ni₂In₄, the more indium-rich Dy₄Ni_10.80In_20.20 structure exhibits a broader range in In-In interactions (291-364 pm). Together the nickel and indium atoms build up polyanionic networks, a two-dimensional one in Dy₅Ni₂In₄ and a complex three-dimensional network in Dy₄Ni_10.80In_20.20. These features have a clear consequence on the dysprosium coordination, i.e. a variety of short Dy-Dy contacts (338-379 pm) in Dy₅Ni₂In₄, while the dysprosium atoms are well separated (430 pm shortest Dy-Dy distance) within the distorted hexagonal channels of the [Ni_10.80In_20.20] polyanion of Dy₄Ni_10.80In_20.20. The crystal chemistry of both structure types is comparatively discussed.     

Structure and magnetic properties of RE2CuIn3 (RE=Ce, Pr, Nd, Sm and Gd)

The ternary copper indides RE₂CuIn₃≡RECu_0.5In_1.5 (RE=Ce, Pr, Nd, Sm and Gd) were synthesized from the elements in sealed tantalum tubes in an induction furnace. They crystallize with the CaIn₂-type structure, space group P6₃/mmc, with a statistical occupancy of copper and indium on the tetrahedral substructure. These indides show homogeneity ranges RECu_xIn_2−x. Single crystal structure refinements were performed for five crystals: CeCu_0.66In_1.34 (a=479.90(7) pm, c=768.12(15) pm), PrCu_0.52In_1.48 (a=480.23(7) pm, c=759.23(15) pm), NdCu_0.53In_1.47 (a=477.51(7) pm, c=756.37(15) pm), SmCu_0.46In_1.54 (a=475.31(7) pm, c=744.77(15) pm), and GdCu_0.33In_1.67 (a=474.19(7), c=737.67(15) pm). Temperature-dependent susceptibility measurements show antiferromagnetic ordering at T_N=4.7 K for Pr₂CuIn₃ and Nd₂CuIn₃ and 15 K for Sm₂CuIn₃. Fitting of the susceptibility data of the samarium compound revealed an energy gap ΔE=39.7(7) K between the ground and the first excited levels.     

Hydroperoxidation of alkanes with hydrogen peroxide catalyzed by aluminium nitrate in acetonitrile

The first example of alkane oxygenation with hydrogen peroxide catalyzed by a non-transition metal derivative (aluminium) is reported. Heating (70 °C) a solution of an alkane, RH, hydrogen peroxide (70% aqueous) and a catalytic amount of Al(NO₃)₃·9H₂O in air for a few hours afforded the corresponding alkyl hydroperoxide, ROOH. With cyclooctane, the hydroperoxide yield attained 31% and the maximum turnover number was 150. It is proposed on the basis of measurements of the selectivity parameters for the oxidation of linear and branched alkanes and a kinetic study that the oxidation occurs with the participation of hydroxyl radicals.     

Rotationally resolved electronic spectroscopy of water clusters of 7-azaindole

The rotationally resolved electronic spectra of the electronic origin of the 7-azaindole-(H(2)O)(1) and of the 7-azaindole-(H(2)O)(2) clusters have been measured in a molecular beam. From the rotational constants the structures in the S(0) and S(1) electronic states were determined as cyclic with the pyrrolo NH and the pyridino N atoms being bridged by one and two water molecules, respectively. Excited state lifetimes of about 10 ns for both clusters have been found. In the spectrum of the 7-azaindole-(H(2)O)(2) cluster a splitting of the rovibronic band is observed, which can be traced back to a large amplitude motion, involving the out-of-plane hydrogen atoms of the water chain. Both the changes of the rotational constants upon electronic excitation and the orientation of the transition dipole point to a solvent induced state reversal between the L(a) and the L(b) states upon microsolvation.     

Anomalously increased lifetimes of biological complexes at zero force due to the protein-water interface

A number of biological bonds show dramatically increased lifetimes at zero-force conditions, compared to lifetimes when even a small tensile force is applied to the ligand. The discrepancy is so great that it cannot be explained by the traditional receptor-ligand binding models. This generic phenomenon is rationalized here by considering the interaction of water with the receptor-ligand complex. It is argued that the water-protein interaction creates an energy barrier that prevents the ligand unbinding in the absence of the force. The properties of the interaction are such that even application of a relatively low force results in a dramatic drop of the bond lifetime due to the alteration of the water-receptor and water-ligand interaction network. The phenomenon is described by the presence of a second shallow interaction energy minimum for the bound ligand followed by a wide receptor-ligand dissociation barrier. The general analysis is applied quantitatively to the actin-myosin system, which demonstrates the gigantic drop of the bond lifetime at small forces and catch behavior (an increase in the lifetime) at moderate forces. The base hypothesis proposed to explain the small-force abnormal drop in the bond lifetime suggests that the majority of biological bonds may exhibit this phenomenon irrespectively whether they behave as slip or catch-slip bonds.